use the number line to identify the least value, first quartile, median, third quartile, and greatest value…

Explanation:

Step1: Sort the data

First, sort the data set (5,5,10,10,15,15,20,20,25,30,30,50).

Step2: Find the least and greatest values

The least value is the first - element of the sorted data, (5). The greatest value is the last - element of the sorted data, (50).

Step3: Calculate the median

Since (n = 12) (even number of data points), the median is the average of the (\frac{n}{2})th and ((\frac{n}{2}+1))th values. (\frac{n}{2}=6), (\frac{n}{2}+1 = 7). The (6)th value is (15) and the (7)th value is (20). Median(=\frac{15 + 20}{2}=17.5).

Step4: Calculate the first quartile

The first quartile (Q_1) is the median of the lower half of the data. The lower half of the data is (5,5,10,10,15,15). Since (n_1=6) (even), (Q_1=\frac{10+10}{2} = 10).

Step5: Calculate the third quartile

The third quartile (Q_3) is the median of the upper half of the data. The upper half of the data is (20,25,30,30,50). Since (n_2 = 6) (even), (Q_3=\frac{25+30}{2}=27.5).

Answer:

least value: (5), first quartile: (10), median: (17.5), third quartile: (27.5), greatest value: (50)